# Vector -- the class of all elements of free modules that are handled by the engine

## Description

If R is a ring handled by the engine, and M is a free module over R, then M is a subclass of Vector.

## Functions and methods returning a vector :

• "Matrix * Vector" -- see * -- a binary operator, usually used for multiplication
• "RingElement * Vector" -- see * -- a binary operator, usually used for multiplication
• "Vector + Vector" -- see + -- a unary or binary operator, usually used for addition
• "Vector - Vector" -- see - -- a unary or binary operator, usually used for negation or subtraction
• - Vector -- negation of a Vector
• "Matrix _ ZZ" -- see generators of ideals and modules
• "Module _ ZZ" -- see generators of ideals and modules
• "homogenize(Vector,RingElement)" -- see homogenize -- homogenize with respect to a variable
• "homogenize(Vector,RingElement,List)" -- see homogenize -- homogenize with respect to a variable
• Matrix Vector (missing documentation)
• "RingMap Vector" -- see RingMap RingElement -- apply a ring map
• "substitute(Vector,List)" -- see substitute -- substituting values for variables
• "substitute(Vector,Matrix)" -- see substitute -- substituting values for variables
• "substitute(Vector,Ring)" -- see substitute -- substituting values for variables
• "substitute(Vector,RingFamily)" -- see substitute -- substituting values for variables
• "super(Vector)" -- see super -- get the ambient module
• Vector ** Vector -- tensor product
• Vector || Vector -- join Vectors
• ZZ _ Module -- integers or zero element

## Methods that use a vector :

• "Ideal * Vector" -- see * -- a binary operator, usually used for multiplication
• "Ring * Vector" -- see * -- a binary operator, usually used for multiplication
• "Vector == Vector" -- see == -- equality
• "contract(Matrix,Vector)" -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• "contract(Number,Vector)" -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• "contract(RingElement,Vector)" -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• "contract(Vector,Matrix)" -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• "contract(Vector,Number)" -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• "contract(Vector,RingElement)" -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• "contract(Vector,Vector)" -- see contract(Matrix,Matrix) -- contract a matrix by a matrix
• "degree(Vector)" -- see degree(RingElement)
• "diff(Matrix,Vector)" -- see diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• "diff(RingElement,Vector)" -- see diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• "diff(Vector,Matrix)" -- see diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• "diff(Vector,RingElement)" -- see diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• "diff(Vector,Vector)" -- see diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• entries(Vector) -- lists the entries of a vector
• "isHomogeneous(Vector)" -- see isHomogeneous -- whether something is homogeneous (graded)
• "leadTerm(Vector)" -- see leadTerm(Matrix) -- get the greatest term of each column
• matrix(Vector) -- make a matrix
• "Module / Vector" -- see Module / Module -- quotient module
• module(Vector) -- the module of a vector
• "norm(Vector)" -- see norm
• "numeric(Vector)" -- see numeric -- convert to floating point
• "numeric(ZZ,Vector)" -- see numeric -- convert to floating point
• "ring(Vector)" -- see ring -- get the associated ring of an object
• "saturate(Vector)" -- see saturate -- saturation of ideal or submodule
• "saturate(Vector,Ideal)" -- see saturate -- saturation of ideal or submodule
• "saturate(Vector,RingElement)" -- see saturate -- saturation of ideal or submodule
• "substitute(Vector,Option)" -- see substitute -- substituting values for variables
• Vector % Ideal (missing documentation)
• Vector ^ List (missing documentation)

## For the programmer

The object Vector is a type, with ancestor classes BasicList < Thing.